Could synchrotron radiation be produced by a gravitational field instead of a magnetic field? I know that synchrotron radiation is produced when a charged particle is accelerated radially by a magnetic field, but I was wondering if synchrotron radiation could also be produced by an uncharged particle radially accelerated by a gravitational field?
Or to put it another way: is synchrotron radiation caused by the radial acceleration of a particle, regardless of the source of acceleration?
 A: I believe that you're essentially asking whether a massive particle orbiting around some gravitational well produces gravitational waves, and the answer in that case is yes.  Imagine that you have two massive objects orbiting each other.  In this case, the system certainly radiates energy in the form of gravitational waves.  Below I have attached a simulated picture of two black holes orbiting each other in two dimensions.  The ripples represent the gravitational waves propagating outward.  Now take the limit as the mass of one of the black holes grows very large.  Now the heavy black hole will barely move and the other one will orbit around it in the same way that a charged particle moves in a synchrotron.  Gravitational waves will still be produced.
Of course, it's worth noting that if you tried to do this with small particles, like neutrons, the gravitational waves would be far too weak to detect.  You would really need very massive objects orbiting very quickly.

A: Okay, I think I'll answer your question with a paper, 
basically I'm doing a dissertation on Gamma Ray Bursts and Gravitational Waves. Look for a paper called 'Gravitational Wave Memory from Gamma Ray Bursts’ Jets' 
It's not mine, I'm referencing it. Basically I think the answer is yes. You will get GWs in your direction if a jet from a gamma ray burst is pointed at you, from the acceleration of the matter. However this would be more symptomatic of Mildly relativistic Cyclotron Radiation rather than full on Synchotron, as the gamma factor is about 100-1000. But for massive 300M collapsars maybe. (sorry for all Jargon, but you wanted to know). However this radiation from these GRBs (Mergers or Stellar Collapse), would be masked by the GWs given out by the Burst, as its far greater in energy.
But to answer your q, Yeah I think they are analogous of eachother. 
PS, I'm here cos I'm looking for the answer to this myself
